ConcepTest 4.6 Force and Two Massesral5q/classes/phys631/summer11/Selecte… · ConcepTest 4.6...
Transcript of ConcepTest 4.6 Force and Two Massesral5q/classes/phys631/summer11/Selecte… · ConcepTest 4.6...
F a1
m1
F m2 m1 a3
1) 3/4 a1
2) 3/2 a1
3) 1/2 a1
4) 4/3 a1
5) 2/3 a1
A force F acts on mass m1 giving acceleration a1.
The same force acts on a different mass m2
giving acceleration a2 = 2a1. If m1 and m2 are
glued together and the same force F acts on this
combination, what is the resulting acceleration?
F
a2 = 2a1m2
ConcepTest 4.6 Force and Two Masses
Mass mm22 must be (1/2)(1/2)mm11 because its
acceleration was 2a2a11 with the same
force. Adding the two masses
together gives (3/2)(3/2)mm11, leading to an
acceleration of (2/3)(2/3)aa11 for the samesame
applied forceapplied force..
F = m1 a1
F a1
m1
F m2 m1 a3
F = (3/2)m1 a3 => a3 = (2/3) a1
1) 3/4 a1
2) 3/2 a1
3) 1/2 a1
4) 4/3 a1
5) 2/3 a1
A force F acts on mass m1 giving acceleration a1.
The same force acts on a different mass m2
giving acceleration a2 = 2a1. If m1 and m2 are
glued together and the same force F acts on this
combination, what is the resulting acceleration?
F
a2 = 2a1m2
F = m2 a2 = (1/2 m1 )(2a1 )
ConcepTest 4.6 Force and Two Masses
ConcepTest 4.7 Climbing the Rope
When you climb When you climb upup a rope, a rope,
the first thing you do is the first thing you do is pullpull
downdown on the rope. on the rope. How doHow do
you manage to go up theyou manage to go up the
rope by doing that??rope by doing that??
1) this slows your initial velocity whichis already upward
2) you don’t go up, you’re too heavy
3) you’re not really pulling down – itjust seems that way
4) the rope actually pulls you up
5) you are pulling the ceiling down
When you pull down on the rope, the rope pulls up on you!!When you pull down on the rope, the rope pulls up on you!!
It is actually this upward force by the rope that makes you
move up! This is the “reactionreaction” force (by the rope on yourope on you)
to the force that you exerted on theyou exerted on the roperope. And voilá, this is
Newton’s 3rd Law.
ConcepTest 4.7 Climbing the Rope
When you climb When you climb upup a rope, a rope,
the first thing you do is the first thing you do is pullpull
downdown on the rope. on the rope. How doHow do
you manage to go up theyou manage to go up the
rope by doing that??rope by doing that??
1) this slows your initial velocity whichis already upward
2) you don’t go up, you’re too heavy
3) you’re not really pulling down – itjust seems that way
4) the rope actually pulls you up
5) you are pulling the ceiling down
FF12 FF21
1) 1) The bowling ball exerts a greaterforce on the ping-pong ball
2) 2) The ping-pong ball exerts a greaterforce on the bowling ball
3) 3) The forces are equal
4) 4) The forces are zero because theycancel out
5) There are actually no forces at all
ConcepTest 4.8a Bowling vs. Ping-Pong I
In outer space, a bowling
ball and a ping-pong ball
attract each other due to
gravitational forces. How
do the magnitudes of these
attractive forces compare?
FF12 FF21
The forcesforces are equal and
opposite by Newton’s 3rd
Law!
1) 1) The bowling ball exerts a greaterforce on the ping-pong ball
2) 2) The ping-pong ball exerts a greaterforce on the bowling ball
3) 3) The forces are equal
4) 4) The forces are zero because theycancel out
5) There are actually no forces at all
ConcepTest 4.8a Bowling vs. Ping-Pong I
In outer space, a bowling
ball and a ping-pong ball
attract each other due to
gravitational forces. How
do the magnitudes of these
attractive forces compare?
ConcepTest 4.10a Contact Force I
If you push with force F on eitherIf you push with force F on either
the heavy box (the heavy box (mm11) or the light) or the light
box (box (mm22), in which of the two), in which of the two
cases below is the contact forcecases below is the contact force
between the two boxes larger?between the two boxes larger?
1) case A1) case A
2) case B2) case B
3) same in both cases3) same in both cases
FF mm22
mm11
AA
FF mm22
mm11
BB
ConcepTest 4.10a Contact Force I
The acceleration of both masses together
is the same in either case. But the contact
force is the onlyonly force that accelerates m1
in case A (or m2 in case B). Since mm11 is the is the
larger masslarger mass, it requires the larger contactlarger contact
forceforce to achieve the same acceleration.
If you push with force F on eitherIf you push with force F on either
the heavy box (the heavy box (mm11) or the light) or the light
box (box (mm22), in which of the two), in which of the two
cases below is the contact forcecases below is the contact force
between the two boxes larger?between the two boxes larger?
1) case A1) case A
2) case B2) case B
3) same in both cases3) same in both cases
FF mm22
mm11
AA
FF mm22
mm11
BB
Follow-up:Follow-up: What is the What is the accelaccel. of each mass?. of each mass?
1) 0 N
2) 50 N
3) 100 N
4) 150 N
5) 200 N
Two tug-of-war opponents each
pull with a force of 100 N on
opposite ends of a rope. What
is the tension in the rope?
ConcepTest 5.3b Tension II
This is literallyliterally the identical situation to the
previous question. The tension is not 200 N !!The tension is not 200 N !!
Whether the other end of the rope is pulled by a
person, or pulled by a tree, the tension in the rope
is still 100 N100 N !!
1) 0 N
2) 50 N
3) 100 N
4) 150 N
5) 200 N
Two tug-of-war opponents each
pull with a force of 100 N on
opposite ends of a rope. What
is the tension in the rope?
ConcepTest 5.3b Tension II
ConcepTest 5.4 Three Blocks
T3 T2 T13m 2m m
a
1) T1 > T2 > T3
2) T1 < T2 < T3
3) T1 = T2 = T3
4) all tensions are zero
5) tensions are random
Three blocks of mass 3m, 2m, and
m are connected by strings and
pulled with constant acceleration a.
What is the relationship between
the tension in each of the strings?
TT11 pulls the wholewhole setset
of blocks along, so it
must be the largestlargest.
T2 pulls the last two
masses, but T3 only
pulls the last mass.
ConcepTest 5.4 Three Blocks
T3 T2 T13m 2m m
a
1) T1 > T2 > T3
2) T1 < T2 < T3
3) T1 = T2 = T3
4) all tensions are zero
5) tensions are random
Three blocks of mass 3m, 2m, and
m are connected by strings and
pulled with constant acceleration a.
What is the relationship between
the tension in each of the strings?
Follow-up:Follow-up: What is What is TT11 in terms of in terms of mm and and aa??
ConcepTest 5.5 Over the Edge
m
10kg a
m
a
F = 98 N
Case (1) Case (2)
1) case 1
2) acceleration is zero
3) both cases are the same
4) depends on value of m
5) case 2
In which case does block m experience
a larger acceleration? In (1) there is a
10 kg mass hanging from a rope and
falling. In (2) a hand is providing a
constant downward force of 98 N.
Assume massless ropes.
In (2) the tension is 98 N
due to the hand. In (1)
the tension is lessless than
98 N because the block
is accelerating downaccelerating down.
Only if the block were at
rest would the tension
be equal to 98 N.
ConcepTest 5.5 Over the Edge
m
10kg a
m
a
F = 98 N
Case (1) Case (2)
1) case 1
2) acceleration is zero
3) both cases are the same
4) depends on value of m
5) case 2
In which case does block m experience
a larger acceleration? In (1) there is a
10 kg mass hanging from a rope and
falling. In (2) a hand is providing a
constant downward force of 98 N.
Assume massless ropes.
ConcepTest 5.12 Will it Budge?
1) moves to the left
2) moves to the right
3) moves up
4) moves down
5) the box does not move
A box of weight 100 N is at
rest on a floor where ms = 0.5.
A rope is attached to the box
and pulled horizontally with
tension T = 30 N. Which way
does the box move?
Tm
Static friction(µs = 0.4 )
The static friction force has a
maximummaximum of mmssN = 40 NN = 40 N. The
tension in the rope is only 30 N30 N.
So the pulling force is not big
enough to overcome friction.
ConcepTest 5.12 Will it Budge?
1) moves to the left
2) moves to the right
3) moves up
4) moves down
5) the box does not move
A box of weight 100 N is at
rest on a floor where µs = 0.4.
A rope is attached to the box
and pulled horizontally with
tension T = 30 N. Which way
does the box move?
Tm
Static friction(µs = 0.4 )
Follow-up:Follow-up: What happens if the tension is What happens if the tension is 35 N35 N? What about ? What about 45 N45 N??
R
vtop
1) 1) FFcc = = TT –– mgmg
2) 2) FFcc = = TT + + NN –– mgmg
3) 3) FFcc = = TT + + mgmg
4) 4) FFcc = = TT
5) 5) FFcc = = mgmg
You swing a ball at the end of stringYou swing a ball at the end of string
in a vertical circle. Since the ball isin a vertical circle. Since the ball is
in circular motion there has to be ain circular motion there has to be a
centripetal force.centripetal force. At the top of the At the top of the
ballball’’s path, what is s path, what is FFcc equal to? equal to?
ConcepTest 5.19c Going in Circles III
R
vTTmgg
You swing a ball at the end of stringYou swing a ball at the end of string
in a vertical circle. Since the ball isin a vertical circle. Since the ball is
in circular motion there has to be ain circular motion there has to be a
centripetal force.centripetal force. At the top of the At the top of the
ballball’’s path, what is s path, what is FFcc equal to? equal to?
FFcc points toward the center of the points toward the center of the
circle, circle, i.ei.e. downward in this case.. downward in this case. The
weight vectorweight vector points downdown and the
tensiontension (exerted by the string) also
points downdown. The magnitude of the
net force, therefore, is: FFcc = = TT + + mgmg
ConcepTest 5.19c Going in Circles III
Follow-up:Follow-up: What is What is FFcc at the bottom of the ballat the bottom of the ball’’s path?s path?
1) 1) FFcc = = TT –– mgmg
2) 2) FFcc = = TT + + NN –– mgmg
3) 3) FFcc = = TT + + mgmg
4) 4) FFcc = = TT
5) 5) FFcc = = mgmg